Recently in [1]}, the authors considered a reduced \(1-\) dimensional model obtained by considering the recovery variable as a parameter. Although not mathematically justified, this assumption is motivated by the observation in [2]} that (REF ) exhibits fast-slow dynamics in particular parameter regimes. This assumption can be justified in suitable parameter regimes using the theory developed in Sections -, i.e. using DGSPT. Specifically, the map in which \(w\)  is treated as a parameter can be viewed as a layer map obtained in the singular limit over regions of \((a,b,c)-\) parameter space such that
\(a w - b v + c = w + \varepsilon g(w,v,\varepsilon ) ,\) 
